<h2>题目编号 : 70</h2>
<div style="color:#666;font-size:80%;">21 May 2004</div><br />
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<p>Euler's Totient function, &phi;(<var>n</var>) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to <var>n</var> which are relatively prime to <var>n</var>. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, &phi;(9)=6.<br />The number 1 is considered to be relatively prime to every positive number, so &phi;(1)=1. </p>
<p>Interestingly, &phi;(87109)=79180, and it can be seen that 87109 is a permutation of 79180.</p>
<p>Find the value of <var>n</var>, 1 <img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /> <var>n</var> <img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /> 10<img src="" style="display:none;" alt="^(" /><sup>7</sup><img src="" style="display:none;" alt=")" />, for which &phi;(<var>n</var>) is a permutation of <var>n</var> and the ratio <var>n</var>/&phi;(<var>n</var>) produces a minimum.</p>

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